We present an analysis of 37 high-quality extended rotation curves that highlight the existence of a new discrepancy (or a new aspect of an old discrepancy) between the density profiles predicted by the lambda cold dark matter (lambda-CDM) theory and the actual distribution of dark matter in galaxies. We compare the predicted face-value density vs. enclosed mass relationship, at large distances, to the observational data at the last measured radii of the rotation curves and in two whole rotation curves of high quality. A further analysis is performed by studying a relation, inbuilt in lambda-CDM, that links, at radius R, the enclosed halo mass MNFW(R) and its density ρ(R) in a way that is independent of the mass of the virialised object. We find that the predicted density vs. enclosed mass relationship has a systematic offset with respect to the observational data. In test case extended rotation curves, at their last measured point, the predicted NFW densities are up to a factor 3 lower than those derived from the kinematics. Moreover, the abovementioned relation, inbuilt in lambda-CDM, does not hold for the objects of our sample. Such a new outer discrepancy is different and maybe complementary with respect to the core/cusp issue, for which the NFW densities turn out to be higher than those observed, and it seems to imply a global mass rearrangement of a pristine NFW-lambda-CDM halo.